Question: 2018 Fall Final - 12
In a standard deck of 52 cards, each card has a suit and a rank.
There are four suits (spades ♠, hearts ♡, clubs ♣, and diamonds ♢),
and 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King).
Assume you get a uniformly random hand consisting of 5 cards. What is the probability that the 5 cards in this hand are all of the same suit?
Assume you get a uniformly random hand consisting of 5 cards. What is the probability that the 5 cards in this hand are all of the same suit?
(a)
$4 \cdot \left. {52 \choose 5} \middle/ {13 \choose 5} \right.$
(b)
$\left. {13 \choose 5} \middle/ {52 \choose 5} \right.$
(c)
$\left. {52 \choose 5} \middle/ {13 \choose 5} \right.$
(d)
$4 \cdot \left. {13 \choose 5} \middle/ {52 \choose 5} \right.$